Turnbull who hosted BBC Breakfast for 15 years prior to the show moving to Salford also fronted Songs of Praise and game show Think Tank.
A spokesperson on behalf of the family said: “Following a challenging and committed fight against prostate cancer, Bill passed away peacefully at his home in Suffolk surrounded by his family on Wednesday, 31 August.
“Bill was diagnosed in 2017 and has had outstanding medical care from the Royal Marsden and Ipswich Hospitals, St Elizabeth Hospice and his GP. He was resolutely positive and was hugely buoyed by the support he received from friends, colleagues, and messages from people wishing him luck. It was a great comfort to Bill that so many more men are now testing earlier for this disease.
“Bill will be remembered by many as a remarkable broadcaster who brought warmth and humour into people’s homes on BBC Breakfast and Classic FM. He was also a devoted Wycombe Wanderers fan and an ever-aspiring beekeeper.
“Bill was a wonderful husband and father to his three children; his family and friends will miss how he always made them laugh, and the generosity and love he shared with those around him.”
BBC Breakfast paid tribute to former presenter Bill Turnbull, who has died aged 66.
A tweet said: “Former BBC Breakfast presenter Bill Turnbull has died. He was 66. He was loved by our viewers. He was loved by his colleagues.
“Bill will always be remembered for his warmth, humour and being a brilliant journalist.”
Paying tribute to Turnbull, former colleague Susanna Reid wrote: “Bill was the kindest, funniest, most generous man in the business. I feel lucky to have worked with him and he taught me everything.
“But above all, he was devoted to his family and I am heartbroken for them. RIP Bill. We will miss you so much.”
The presenter revealed his prostate cancer diagnosis in March 2018, saying he was diagnosed the previous November, and he detailed his treatment in a Channel 4 documentary called Staying Alive.
In October last year he announced he was taking a leave of absence from his show on Classic FM for health reasons.
Announcing the news on social media, Turnbull said he was taking “a leave of absence” from his weekend programme, which he had fronted for five years.
He started his broadcast career at Scotland’s Radio Clyde in 1978, joining the BBC as a reporter for the Today programme in 1986 before becoming a reporter for BBC’s Breakfast Time two years later.
In 1990, Turnbull, who went to university in Edinburgh, became a correspondent for BBC News and reported from more than 30 countries.
In 2005, he competed as a contestant on Strictly Come Dancing partnered with Karen Hardy, and was the seventh celebrity voted off the show.
Other TV appearances include Who Wants To Be A Millionaire? and Through The Keyhole; the BBC’s Celebrity Mastermind, Would I Lie To You?, Pointless Celebrities and Room 101, and Channel 4′s Countdown.
In 2011 he appeared in the Doctor Who episode The Wedding Of River Song.
During his time on BBC Breakfast, he presented alongside Sian Williams, Susanna Reid, Kate Silverton, Natasha Kaplinsky and Louise Minchin.